Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[     [2],    [3,4],   [6,5,7],  [4,1,8,3]]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

#include<iostream>#include<vector>/************************************************************************//* 这个版本虽然简单，但是测试数据：[[46],[43,61],[10,-16,3],[-26,41,36,-72],[-28,-76,-22,26,51],[56,-53,38,67,86,-45],[58,53,47,-52,-54,-95,56],[-54,-93,58,68,26,-4,-45,86],[75,28,27,12,33,98,35,87,1],[-13,20,25,-98,-13,11,-44,-77,-59,-97],[-53,-14,83,80,31,89,38,-1,15,-88,53],[-22,86,-41,-94,-25,68,-96,87,55,-18,-49,-25],[-93,-48,39,17,8,61,57,-13,-92,-79,-29,87,51],[-63,3,-72,29,-9,57,-93,-46,-84,88,29,83,69,-7],[15,-49,43,90,-43,94,29,50,-21,-33,-16,43,-26,4,90],[-61,-67,-96,18,-63,32,-91,93,16,-61,86,4,67,46,-27,-63],[-38,0,79,-48,56,51,80,-17,-70,-53,67,49,-3,-52,39,12,-43],[43,-93,-7,-48,91,-13,44,-69,-27,-74,74,95,-25,-88,-43,75,90,8],[8,41,-35,91,48,-12,35,-3,62,59,-86,-49,-83,56,-42,-14,84,-74,72],[6,-44,-78,31,-92,-82,-94,-81,-49,57,85,36,-34,4,77,-66,-71,-34,45,25],[-95,4,15,-45,-3,-52,-11,83,-67,15,32,38,47,54,-54,54,48,-72,72,75,85],[35,11,-72,-61,-11,-62,-33,31,82,68,35,-37,-16,66,37,31,-44,20,40,47,-71,-45],[-6,59,0,-51,7,5,97,-40,-10,32,70,-6,47,-41,31,-86,89,-10,59,1,29,-57,-32],[-34,73,0,62,-9,-53,91,45,17,50,-54,65,-65,50,40,-6,-83,-28,-59,-13,-80,0,94,-90],[-34,-39,68,67,89,-89,-88,-67,61,-12,71,-48,11,62,73,-72,-10,95,70,1,45,10,71,38,58],[-88,-98,54,-12,95,64,31,-44,9,-25,-77,20,-14,-45,-42,73,-74,-14,-16,65,-41,-12,-68,-45,-42,32],[76,44,-20,-8,3,-32,-7,-66,56,-11,97,-36,21,7,38,43,-96,-76,74,-62,73,-99,0,-66,42,58,21],[73,89,56,-18,43,0,61,-65,79,-71,27,-86,61,92,87,-98,-9,-29,39,-89,-49,39,85,-12,12,62,87,45],[4,23,-56,-46,12,99,35,-45,-24,-27,-34,-44,1,70,-54,-60,39,-67,-59,-70,-19,57,-59,31,-4,-97,96,85,64],[83,7,-55,-17,50,-2,72,49,-67,-96,-74,5,-30,-42,82,-60,3,98,78,12,-83,85,92,73,-97,24,-54,-95,20,-69],[45,-20,38,89,63,-12,-36,35,-85,-27,38,-83,77,84,-26,36,-99,53,12,56,-35,5,41,-42,-22,43,58,0,24,-45,31],[-31,34,-31,-65,-26,33,-2,85,24,70,1,40,24,-15,90,-63,-14,20,48,-81,85,-47,59,-80,7,-21,54,-92,-97,-91,15,-52],[19,60,-18,93,-30,79,55,94,49,-44,11,-27,18,-21,9,80,98,-65,98,60,-36,34,56,71,-87,10,55,-85,-5,-53,-38,-85,-93],[43,84,-47,-1,39,-53,-52,72,35,-3,-10,-86,82,-30,88,-83,-55,49,-19,78,5,-71,90,92,60,81,-13,-93,-80,1,89,39,-38,-81],[-62,-98,-57,-38,73,77,58,-60,67,40,-14,55,34,30,-19,91,-15,63,-80,-25,55,79,-67,-81,62,-71,-3,28,67,58,46,81,59,88,-57],[9,42,77,48,9,-6,-89,-58,-72,40,22,-81,-98,-15,-85,-24,-83,70,-15,-64,32,13,32,-63,-20,-10,60,-62,-73,48,-20,12,-9,-43,-62,76],[51,-52,-82,55,65,40,74,66,-98,88,-80,-81,59,4,-46,-32,94,62,5,-49,-48,-35,-11,-45,89,68,67,-43,-97,-95,-66,53,-71,-49,-15,93,67],[-41,37,69,-75,56,87,83,-63,-82,-49,-69,79,32,-18,-92,73,70,-37,63,15,-93,-80,17,87,-70,-53,-84,-42,32,86,-75,67,23,70,91,-44,34,51],[-8,51,79,23,7,11,81,-8,-38,28,31,-75,-57,37,-79,37,24,-72,60,16,-15,-31,-21,9,-63,-98,-43,-72,-43,90,79,49,19,58,-51,-74,-54,-93,-6],[7,34,-75,8,76,61,6,-10,-38,33,-49,55,-82,19,-66,3,32,-87,59,60,-31,27,16,94,-54,-49,-80,-52,-27,-74,42,80,59,66,-35,13,5,70,-97,43],[-20,-70,-25,-26,26,9,77,-42,21,13,94,66,-83,10,61,-38,37,57,-13,-89,83,-71,67,19,71,-91,-68,-47,79,-88,73,-41,-82,-52,33,43,56,-13,-98,-46,76],[72,-79,93,-17,58,-68,96,-8,18,-93,-25,23,50,71,-28,59,-97,1,15,90,-26,50,85,22,-17,28,-45,46,6,-14,0,-21,6,-30,38,-59,1,34,32,96,18,84],[-4,-32,55,67,-73,34,-54,18,2,19,-31,-13,-82,28,-85,-27,-25,-2,35,51,53,-59,-79,-9,-42,21,-98,66,-6,19,27,90,64,-18,34,67,93,79,-14,-5,-24,54,81],[-7,-18,72,42,33,-30,-23,-16,-77,-6,4,-10,28,-97,-8,-5,-4,-89,-78,-14,74,-19,97,42,-26,76,-72,68,-48,58,49,45,-60,-2,-36,73,68,41,-43,67,-65,38,-42,63],[40,49,-65,-64,36,-67,-1,-12,13,-4,-70,86,-51,-66,31,1,91,-43,-77,-69,55,-14,80,23,-96,-85,-33,-84,52,24,55,-8,-50,89,4,63,-78,79,-49,12,-25,-43,-25,24,-10],[-93,-98,-42,-37,-76,-35,-82,-14,-54,17,-10,-40,84,5,88,8,-40,-20,35,-74,60,-2,-76,40,48,35,91,-95,-89,-8,-29,93,-7,28,-44,-7,69,-26,79,91,67,-54,-72,51,27,-84],[-63,63,-28,71,65,-67,-54,88,49,93,1,40,74,-12,-90,-55,-19,2,49,13,72,-5,86,28,-13,31,73,14,-18,-23,30,18,-60,78,-34,-95,-89,11,69,36,4,-30,-23,-45,34,-14,-1],[-85,64,-75,28,13,20,-9,-59,83,-78,90,-3,-19,-33,-96,98,-17,59,-35,-36,69,75,-89,-17,-43,-43,36,11,91,98,87,82,62,88,-13,-24,-15,55,-7,-32,53,-16,42,-66,27,22,-67,87],[-19,-26,-49,-72,-51,-39,10,-18,18,-54,93,-14,-56,57,-32,82,45,55,-65,-69,-13,28,-25,-60,88,-83,-26,-8,16,6,-21,96,56,7,-99,81,67,10,-36,-38,32,-66,24,75,90,69,35,12,24],[69,19,-89,-26,71,-50,-61,87,0,31,-20,82,-90,-46,38,16,-46,20,-39,64,60,-1,-4,93,-99,-51,60,69,83,-51,-7,29,68,-20,80,39,6,-81,3,-93,49,60,65,36,-86,4,-71,-33,-99,-34],[-69,60,42,4,30,42,52,-10,11,12,15,80,-82,-17,-40,97,98,42,-83,-21,25,42,-61,-9,-45,-48,71,-16,18,71,26,26,31,-32,-93,-39,-90,35,27,20,-53,-58,0,-36,2,36,-61,-23,-44,-45,55],[80,73,93,-52,-71,-78,-81,12,17,66,-85,-80,-3,-17,-74,34,-8,60,-62,-87,83,-20,-11,-76,58,-74,-38,-65,-19,16,90,-62,-33,60,-37,-5,82,-42,83,-24,-75,97,-5,-2,-20,20,-67,72,-43,-30,61,-60],[26,-50,-37,-16,-25,25,19,32,-82,-14,70,-16,-54,-90,78,-95,-33,61,-20,-9,36,51,66,-84,-29,75,64,27,-55,25,43,48,52,-93,-91,-96,31,27,36,48,-87,-17,-90,-64,-8,87,-83,35,26,-3,-96,-38,-75],[69,-46,-27,44,95,76,65,2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dfsPath(vector<int> &path,int upperPos,vector<vector<int> > &triangle,int currentLevel,int &minValue){if(currentLevel >= triangle.size()){int tempValue=0;for(int i=0;i<path.size();i++){tempValue += path.at(i);}if(tempValue < minValue)minValue = tempValue;return;}path.push_back(triangle[currentLevel][upperPos]);dfsPath(path,upperPos,triangle,currentLevel+1,minValue);path.pop_back();path.push_back(triangle[currentLevel][upperPos+1]);dfsPath(path,upperPos+1,triangle,currentLevel+1,minValue);path.pop_back();}int minimumTotal(vector<vector<int> > &triangle) {if(triangle.size() <= 0)return 0;if(triangle.size() == 1)return triangle[0][0];vector<int> path;int upperPos = 0;int currentLevel = 1;int minValue = INT_MAX;path.push_back(triangle[0][0]);dfsPath(path,upperPos,triangle,currentLevel,minValue);return minValue;}*//************************************************************************//************************************************************************//*这个版本执行速度也很快的，时间复杂度为O(n)，n为元素的个数。空间复杂度也很低的。但是因为是建立在修改原有数据的基础上的。在这个原则上，算法不是很好的。原则上是top->downint minimumTotal(vector<vector<int> > &triangle) {if(triangle.size() <= 0)return 0;if(triangle.size() == 1)return triangle[0][0];int minValue = INT_MAX;for(int i=1;i<triangle.size();i++){for(int j=0;j<triangle[i].size();j++){int upperLeftSum=INT_MAX,upperRightSum=INT_MAX;if(j-1>=0){upperLeftSum = triangle[i-1][j-1]+triangle[i][j];}if(j < triangle[i-1].size()){upperRightSum = triangle[i-1][j]+triangle[i][j];}triangle[i][j] = min(upperLeftSum,upperRightSum);if(i == triangle.size()-1){if(minValue > triangle[i][j])minValue = triangle[i][j];}}}return minValue;}*//************************************************************************/using namespace std;/************************************************************************//*这个方法比较经典的利用的思路是down->topminV[k][i] = min(minV[k+1][i],minV[k+1][i+1])+triangle[k][i]*//************************************************************************/int minimumTotal(vector<vector<int> > &triangle) {int n = triangle.size();vector<int >minlen(triangle.back());for(int i=n-2;i>=0;i--){for(int j=0;j<triangle[i].size();j++){minlen[j] = min(minlen[j],minlen[j+1])+triangle[i][j];}}return minlen[0];}int main(void){vector<vector<int> > triangle;vector<int > temp;temp.push_back(2);triangle.push_back(temp);temp.clear();temp.push_back(3);temp.push_back(4);triangle.push_back(temp);temp.clear();temp.push_back(6);temp.push_back(5);temp.push_back(7);triangle.push_back(temp);temp.clear();temp.push_back(4);temp.push_back(1);temp.push_back(3);temp.push_back(8);triangle.push_back(temp);temp.clear();cout << minimumTotal(triangle) << endl;system("pause");return 0;}